Protesters march in Brussels to demand a government. Photograph: Julien Warnand/AFP/Getty Images

Tens of thousands of protesters marched through the Belgian capital today in support of national unity and to demand that the rival political groups form a coalition after seven months without a government.

Organisers said the peaceful rally in Brussels was also meant to promote solidarity among the country's Flemish and Walloon communities and to reject nationalism.

Police said between 20,000 and 30,000 people took part in the demonstration called by a group of university students who say they are fed up with the political deadlock.

"We're sending a clear message to the political leaders that we want them to form a government," said Felix De Clerck, one of the organisers.

"We are sick and tired of the enduring political impasse," said Thomas Decreus, another organiser. He said the protest showed "the people can act where politicians fail: ie working together across the language barrier" that slices Belgium in half.

The demonstration – the result of a Facebook campaign under the banner "Shame. No government, great country" – was the second of its kind in just over three years. On 18 November 2007, about 35,000 people marched through the capital to vent their anger about a political deadlock that by then was preventing the formation of a government for 161 days.

Like in 2007, today's protest led demonstrators – Francophones and Dutch-speakers – to a vast stone arch in the Cinquantenaire park. The arch marks Belgium's independence from the Netherlands in 1830 .

Political parties representing Belgium's two communities have been unable to form a coalition since parliamentary elections last June – a record period of deadlock in postwar Europe.

Politicians have been trying unsuccessfully to broker a new constitution with increased regional autonomy for the 6 million Dutch-speaking Flemings and 4.5 million French-speaking Walloons.

The deadlock has led to fear that Flanders could secede from the union formed in 1830.

Positions in Flanders have hardened over the years, bringing to the fore the centre-right N-VA nationalist party headed by Bart De Wever. He is negotiating on forming a government with the socialist PS party, the dominant political party in Wallonia.

In a reference to De Wever, several demonstrators carried pictures of cartoon character Bart Simpson with his face crossed out. Others carried signs saying "Separation? Not in our Name," and "Less Bla-Bla, More Results."

Many carried umbrellas, hats, shawls and other items in the black, gold and red colours of the Belgian flag. "What do we want? We want a government," they chanted.

Since the elections, the country has been run by a caretaker government led by the prime minister, Yves Leterme. But that government only has a limited remit and, as the euro currency tries to weather a deepening crisis, international investors are looking unkindly at the political stalemate that hamstrings the nation and prevents it from taking decisive action.